In this post, I questioned the constitutionality under the 17th Amendment of proposed congressional legislation requiring states to hold an election to fill an open Senate seat within 90 days of the vacancy. I did not see this as within the time, place, and manner powers of Congress to regulate congressional elections in light of the 17th Amendment’s specific language giving the power of filling vacancies and making temporary appointments to the states (and potentially to the state’s governors).
A reader points me to Vik Amar’s testimony before a joint congressional committee in which he (surprisingly, to me) comes out the other way. A snippet:

The question of Congressional power over vacancy-filling Senate elections may seem a bit trickier. Certainly, Congress under the original Constitution had the power to regulate the timing of all Senate elections done by state legislatures, including elections done by state legislatures to fill unexpected vacancies. Indeed, Congress in 1866 passed an Act that regulated the manner and timing of all state legislative elections of U.S. Senators. The Act said that whenever there was a Senate vacancy of any kind, both houses of a state legislature, on the second Tuesday they were in session, must vote to fill the vacancy, and if no person was elected, both houses must continue to vote at least once each and every day thereafter of the legislative session.
Do the text and timing of the Seventeenth Amendment change any of this? I think the answer is “no.” As for text, it is true that the last words of the vacancy-filling provision of the Seventeenth Amendment – “by election as the legislature may direct: – suggest that state legislatures enjoy discretion. To be sure, the phrase “as the legislature[] thereof may direct” or “as the Congress may direct” used elsewhere in the Constitution connote broad independence and leeway. For example Article II’s use of the phrase “as the legislature[] thereof may direct” has been interpreted by the Supreme Court in Bush v. Gore as giving state legislatures extremely wide latitude in picking Presidential electors. But the key difference is that in the Presidential election context, state legislative discretion is not superseded by explicit Congressional power embodied in Article I, Section 4. Article I, Section 4 itself says state legislatures have power to prescribe times, places and manners – broad leeway – but that such power can be overridden by Congressional exercise. So even though the “as the legislature may direct” language of the Seventeenth Amendment connotes state legislative power, if that power is constrained by Article I, Section 4, then the Seventeenth Amendment provides no barrier to statutes like E.L.E.C.T.
But can we apply Article I, Section 4 Congressional power to a provision of the Constitution enacted after Article I was adopted? Grammatically we surely can. Article I, Section 4, speaks broadly of Congress’ power to “alter or make” “at any time” the regulations concerning the time of “holding elections for Senators and Representatives” – not just some temporal or geographical subset of Senators or Representatives.
Moreover, everyone seems to agree that we can and do apply Article I, Section 4 to regularly scheduled (every six year) Senate elections held by the people of each state, even though these popular elections are created and provided for only in the Seventeenth Amendment, adopted after Article I, Section 4. And there is nothing in the text of the Seventeenth Amendment that distinguishes regular popular elections from vacancy-filling popular elections. If Article I, Section 4 applies to the former, it ought to apply to the latter as well, and there are no words in or legislative history of the Seventeenth Amendment to suggest otherwise.
Indeed, the legislative history strongly favors applying Article I, Section 4 to all of the Seventeenth Amendment’s provisions. Southern Senators attempted, during the latter stage debates over the Seventeenth Amendment, to insert language that would have freed popular elections of Senators from Congressional control under Article I, Section [4].

I will want to hear more about the legislative history. But on the textual argument, I’m not convinced. It looks like the 17th amendment provides a specific rule related to a narrow question–the timing and means of filling vacant Senate seats–which by implication supersedes the Article I, section 4 powers.
It is worth looking at the other testimony from the hearing as well, including from Pam Karlan.